| Summary: | A Dissertation submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg,
in ful llment of the requirements for the degree of Master of Science.
January 2017 === In this dissertation, we will develop novel methods for determining the spectrum of primary
operators in a free conformal eld theory (vector model) and to construct some of these
primaries. To count the spectrum of primaries, we use group theoretic techniques to obtain
character formulas for any number of elds as representations of SO(4; 2). More precisely,
we will construct generating functions that can be expanded to any order in the conformal
scaling dimension to yield the complete spectrum of primaries constructed out of n scalar
elds. We also develop e cient methods to construct these primaries by using a polynomial
description. Finally, these primary operators, which are higher spin currents in the free
conformal vector model, correspond to higher spin gauge elds in Vasiliev higher spin theory
through the holographic duality. === MT 2017
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